[en] In view of applications to fermions, an anticommutative mechanics is constructed with new Euler-Lagrange equations, action theorem, ... In this new 'anti-mechanics', Lagrangians, currents, conserved integrals, are antisymmetric forms. By 'tensor product' with usual mechanics, the 'super-mechanics' suggested by J. Schwinger can be constructed

[en] We reformulated the fractional free electromagentic lagrangian density using the radiation (Coulombo) gauge and lorentz gauge. We also obtained fractional Euler-lagrange E-L) equations resulting from these Lagrangian densities. Then we found fractional Hamiltonian density in general form and used dirac algebraic methods to determine the creation and annihilation operators to construct the Canonical Commutation relations (CCRs). (authors).

[en] Lagrangian point of view on conformally invariant nonrelativistic dynamics is presented

[en] Following recent claims relative to the question of large anisotropy production in regular bouncing scenarios, we study the evolution of such anisotropies in a model where an ekpyrotic phase of contraction is followed by domination of a Galileon-type Lagrangian which generates a non-singular bounce. We show that the anisotropies decrease during the phase of ekpyrotic contraction (as expected) and that they can be constrained to remain small during the non-singular bounce phase (a non-trivial result). Specifically, we derive the e-folding number of the phase of ekpyrotic contraction which leads to a present-day anisotropy in agreement with current observational bounds. Communicated by P Singh (paper)

[en] We generalize Hamilton's principle with fractional derivatives in the Lagrangian L(t, y(t), ₀D^α_ty(t), α) so that the function y and the order of the fractional derivative α are varied in the minimization procedure. We derive stationarity conditions and discuss them through several examples.

[en] Another lagrangian which uses the Louis de Broglie wavelength is substituted to the relativist lagrangian L. They are identical for free particle only. A charged particle is situated in an electrostatic field. When internal energy is high relative to electrostatic energy, the function L is consequently the principal part of a more extensive lagrangian of variable mass which explains the phase velocity V of the associated wave

[en] The equivalence of Lagrangian and Hamiltonian quantization for the singular theories with second class constraints only is proved

[en] We study the topology of adjacencies of multisingularities in the image of a stable Lagrangian map with singularities of types $A_{\mathrm{\mu <!--\; ??\; -->}}^{\pm <!--\; ??\; -->}$ and $D_{\mathrm{\mu <!--\; ??\; -->}}^{\pm <!--\; ??\; -->}$. In particular, we prove that each connected component of the manifold of multisingularities of any fixed type $A_{{\mathrm{\mu <!--\; ??\; -->}}_1}^{\pm <!--\; ??\; -->}\cdots <!--\; ???\; -->A_{{\mathrm{\mu <!--\; ??\; -->}}_p}^{\pm <!--\; ??\; -->}$ for a germ of the image of a Lagrangian map with a monosingularity of type $D_{\mathrm{\mu <!--\; ??\; -->}}^{\pm <!--\; ??\; -->}$ is either contractible or homotopy equivalent to a circle. We calculate the number of connected components of each kind for all types of multisingularities. As a corollary, we obtain new conditions for the coexistence of Lagrangian singularities.

[en] Short communication; 3 refs

[en] We have supersymmetrize the famous horizontality condition in order to derive the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRSTsymmetry transformations for the Supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. The most important feature of this investigation is the derivation of a Curci-Ferrari (CF) type of restriction which is responsible for the absolute anticommutativity and the existence of coupled (but equivalent) Lagrangian for the present Supersymmetric system. (author)